Page 207 - DSP Integrated Circuits

192 Chapter 5 Finite Word Length Effects

The input signal is shown in Figure
5.6. If no precautions are taken, the filter
will enter into a parasitic overflow oscilla-
tion. The magnitude and spectrum of the
oscillation will depend on the state of the
filter at the moment the input becomes
zero.
Figure 5.6 also shows the output sig-
nal when the number range has been lim-
ited using saturation arithmetic. In this Figure 5.5 Second-order section with
case, the use of saturation arithmetic is saturation arithmetic
sufficient to suppress the large parasitic
overflow oscillation, but not completely.

Figure 5.6 Parasitic overflow oscillation with and without saturation arithmetic

Parasitic oscillations can not, in general, be suppressed in higher-order struc-
tures by using saturation arithmetic, except for state-space structures [14,32] and
wave digital filters. The hardware expense for implementing saturation arithmetic
is often non-negligible. The execution time required for standard signal processors
that do not have built-in instructions with conditional saturation and quantization
instructions is significant.